The global spread of COVID-19 had severe consequences for public health and the world economy. The quick onset of the pandemic highlighted the potential benefits of cheap and deployable pre-screening methods to monitor the prevalence of the disease in a population. Various researchers made use of machine learning methods in an attempt to detect COVID-19. The solutions leverage various input features, such as CT scans or cough audio signals, with state-of-the-art results arising from deep neural network architectures. However, larger models require more compute; a pertinent consideration when deploying to the edge. To address this, we first recreated two models that use cough audio recordings to detect COVID-19. Through applying network pruning and quantisation, we were able to compress these two architectures without reducing the model's predictive performance. Specifically, we were able to achieve an 105.76x and an 19.34x reduction in the compressed model file size with corresponding 1.37x and 1.71x reductions in the inference times of the two models.